ānupubbī-kathā: 'gradual instruction', progressive sermon; given by the Buddha when it was necessary to prepare first the listener's mind before speaking to him on the advanced teaching of the Four Noble Truths. The stock passage (e.g. D. 3; D 14; M. 56) runs as follows:

"Then the Blessed One gave him a gradual instruction - that is to say, he spoke on liberality ('giving', dāna, q.v.), on moral conduct (sīla) and on the heaven (sagga); he explained the peril, the vanity and the depravity of sensual pleasures, and the advantage of renunciation. When the Blessed One perceived that the listener's mind was prepared, pliant, free from obstacles, elevated and lucid; then he explained to him that exalted teaching particular to the Buddhas (buddhānaṃ sāmukkaṃsikadesanā), that is: suffering, its cause, its ceasing, and the path."

Buddhist Dictionary, Manual of Buddhist Terms and Doctrines, by NYANATILOKA MAHATHERA